MTH 218-6816
Exam1
February23, 20IL
ProfesserIlva Kofman
NAME:
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Problem 1.
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S u p p o se
C E = A D = B F andCEllADllBF.
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A
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Tf BCEF is a rectangle,what is this figure calledpreciseiy?
(b) If. ZCBF is obtuse,what is this figure called precisely?
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Verify Euler's formula for this figure.
Problem 2. (r) If a prism has a 50-gon for its base,how many vertices,edges
and facesdoesit have? Verify Euler's formula for this prism.
(b) If a prism has 120 edges,how many vstices and facesdoes it have? Verify
Eulerls formula for this prism.
Problem 3. (") What is the measureof an interior angleof a regular decagon?
(b) Explain why it cannot be the face of a regular poiyhedron.
I
Problem 4. One semiregulartiling of the plane consistsof these three regular
polygonsat everyvertex: a dodecagon(12-gon),a square,,andwhat other polygon?
Justify.
Problem 5. Considerthe earthand moonasshown.
(a) Is the moonr,.*,
|, ;,
(b) Is it-waxingor waning?
<*.
+- (
ln,or tull?
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(**rr
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Problem 6. Find the missing anglemeasuresindicated by letters in the diagram
below. Two parallel lines are indicated by arrows.
4=
b:
ee
J=
e" ="
F
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$e
Problem 7. Convexor concave?
(a) Thapezoid
(b) Obtusetriangle
(c) Two regular hexagonsgiued along a common edge
(d) Regularpoiyhedron
(e) Oblique pyramid
Problem 8. For each of the foliowing pairs, identify which type of Venn diagram
describestheir relationship.
co
overlapping
disjoint
o
subset
(a) Rectanglesand kites
(b) Rhombi and parallelograms
(c) Rhombi and quadrilateralswith congruentdiagonals
(d) Reetanglesand trapezoids
(e) Kites and squares
(f) Isosceles
trianglesand obtusetriangles
(g) Regular polyhedra and pyramids
(h) Prismsand pyramids
Problem 9. Among parallelograms, rectangles,rhombi, and isoscelestrapezoids,
list all for which the following statements always true:
(a) Adjacent anglesare congruent.
(b) Opposite anglesare congruent.
(c) Diagonalsbisect angles.
(d) Diagonals are congruent.
(e) Diagonalscrossat right angles.
(f) Diagonalscrossat midpoints.
Pro b l e m 1 0 . In L A B C,IA:30' and
lB:70o. UseeitherEuclid' sPar al l el
Postulateor the rotation anglesmethod to preciselyexplain why lC: 80o.
AC
T
Compass and straightedge constructions. Please number your arcs.
Problem LL.
Preciselybisectthis angle.
c
Problem 12.GivensegmentAB and point C.
Construct a line parallel to AB
through C by copying an angle.
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A
Problem 13.
E
F
Construct a squarewith given side EF.
Problem 14. P
Construct a regular hexagonwith given side PQ.
Hint: First construct an equilateraitriangle.
B